Names of units of some physical quantities are given in List-$I$ and their dimensional formulae are given in List-$II$. Match the correct pairs in the lists:

$A$. $Pa \cdot s$	$(i)$. $[L^2 T^{-2} K^{-1}]$
$B$. $N \cdot m \cdot K^{-1}$	$(ii)$. $[MLT^{-3} K^{-1}]$
$C$. $J \cdot kg^{-1} \cdot K^{-1}$	$(iii)$. $[ML^{-1} T^{-1}]$
$D$. $W \cdot m^{-1} \cdot K^{-1}$	$(iv)$. $[ML^2 T^{-2} K^{-1}]$

Pressure exerted by a gas is found to be $50\, N/m^2$. What is the value of this pressure in the $CGS$ system?

Match the following?

Column-$I$	Column-$II$
$(a)$ Ratio of change in time period of a simple pendulum with temperature to its original time period	$(i) \, \alpha \Delta T$
$(b)$ Ratio of the value of a length to its scale reading	$(ii) \, T$
$(c)$ Reciprocal of coefficient of volume expansion for an ideal gas of constant pressure	$(iii) \, (1 + \alpha \Delta T)$
$(d) \, \frac{F}{YA} =$	$(iv) \, \frac{1}{2} \alpha \Delta T$

The related effort to derive the properties of a bigger,more complex system from the properties and interactions of its constituent simpler parts is:

Just as precise measurements are necessary in science,it is equally important to be able to make rough estimates of quantities using rudimentary ideas and common observations. Think of ways by which you can estimate the following (where an estimate is difficult to obtain,try to get an upper bound on the quantity):
$(a)$ The total mass of rain-bearing clouds over India during the Monsoon.
$(b)$ The mass of an elephant.
$(c)$ The wind speed during a storm.
$(d)$ The number of strands of hair on your head.
$(e)$ The number of air molecules in your classroom.

Some physical quantities are given in Column $I$ and some possible $SI$ units in which these quantities may be expressed are given in Column $II$. Match the physical quantities in Column $I$ with the units in Column $II$.

Column $I$	Column $II$
$(A)$ $GM_e M_s$ ($G$: universal gravitational constant,$M_e$: mass of the earth,$M_s$: mass of the Sun)	$(p)$ $(\text{volt})(\text{coulomb})(\text{metre})$
$(B)$ $\frac{3RT}{M}$ ($R$: universal gas constant,$T$: absolute temperature,$M$: molar mass)	$(q)$ $(\text{kg})(\text{m})^3(\text{s})^{-2}$
$(C)$ $\frac{F^2}{q^2 B^2}$ ($F$: force,$q$: charge,$B$: magnetic field)	$(r)$ $(\text{m})^2(\text{s})^{-2}$
$(D)$ $\frac{GM_e}{R_e}$ ($G$: universal gravitational constant,$M_e$: mass of the earth,$R_e$: radius of the earth)	$(s)$ $(\text{farad})(\text{volt})^2(\text{kg})^{-1}$